1. Field of Invention
The present invention relates to Image Metrology and more particularly to six degree-of-freedom (DOF) spatial measurement from images using an Orientation Dependent Radiation (ODR) Source. The Orientation Dependent Radiation is used to accurately determine the ODR Source's pose from an image. The invention relates more particularly to improvements to the apparatus of the ODR Source and the methods of interpreting an image of the ODR Source to simplify the analysis and improve the accuracy of orientation measurement, and to resolve the Cosine Ambiguity.
2. Discussion of Relevant Prior Art
Orientation Dependent Radiation (ODR) sources are known to the prior art. There construction and use is taught in U.S. Pat. Nos. 5,936,722, 5,936,723 and 6,384,908.
The prior art is illustrated in FIGS. 1 to 2. In FIG. 1, there are a plurality of ODR Regions and each region contains ODR Patterns. ODR Patterns (104) are schematically illustrated in FIG. 1. The Orientation Dependent Radiation Pattern is an approximately sinusoidal pattern of radiation which covers the entire ODR Region.
Each ODR Pattern includes a Detectable Property, such as pattern Phase Angle that can be measured from an image and used to determine the out-of-plane rotation of the ODR Source. The out-of-plane rotation generally can not be accurately measured without the use of Orientation Dependent Radiation. For example, the ODR Patterns give rise to an approximately sinusoidal pattern of intensity running along the length of each Longitudinal Axis of the patterns. Each ODR Region has a Longitudinal Axis (102) as shown schematically in FIG. 1. The Detectable Property is measured at a Point of Measurement (103), such as shown in FIG. 1 and in FIG. 2.
Landmarks (110) in FIG. 1, are used to determine the locations of the ODR source in an image, and to determine the locations of features in the image, such as lie of a Longitudinal Axis (102) and the Point of Measurement (103).
One significant feature in the image is the Point of Measurement (103) in FIG. 1 and FIG. 2. This is the point at which the Detectable Property of the Orientation Dependent Radiation is determined.
Those skilled in the arts will be aware that a Detectable Property measured at a Point of Measurement (103) in the image will depend upon the precise location in the image of that Point of Measurement. If Point of Measurement (103) is shifted, an error of measurement will arise.
Elements of the process of locating Point of Measurement (103) are illustrated in FIG. 2. Landmarks (110) are detected and located by image processing. The locations of the Landmarks (110) in the image are used to determine the Point of Measurement (103) in each of the ODR Regions (101). Only the process of locating Point of Measurement (103) for the upper right Orientation Dependent Radiation Pattern pictured in FIG. 1 is shown. The processes of locating any other Point of Measurement (103) follow, mutatis mutandis.
The process illustrated in FIG. 2 involves projecting the measured locations of Landmarks (110) along lines (202) drawn in the image to the Point of Measurement (103). In this projection process, inevitable small errors in the measured location of the Landmarks result in larger errors in determination of the Point of Measurement (103). Indeed, those skilled in the art of Image Metrology will realize that the errors in determining the location of the Point of Measurement (103) will be at least several times as great as the error in determining the location of any one Landmark. If the Landmark were located at the Point of Measurement (103), this compounding of small errors into large errors could be avoided. But the prior art offers no means to locate Landmarks at the Points of Measurement.
It is also well known to those skilled in the art of Image Metrology that features on the back (161b) of a Transparent Substrate which is tilted with respect to a camera appear shifted in an image relative to features on the front (163b) of the Transparent Substrate, as shown in FIG. 8. The magnitude of shift depends on the thickness and index of refraction of the substrate, in a well known way. This shift of the apparent position of a Landmark is hereinafter referred to as the Back-to-Front shift.
For Landmarks to be useful for accurately locating the Point of Measurement, they must lie on the observation surface of the target. This is because the Back-to-Front shift can not be accurately determined while the tilt of the ODR Source is unknown. And the Point of Measurement must be used to determine the Detectable Property of the Orientation Dependent Radiation, and thereby determine the tilt of the ODR Source. Thus, Landmarks used to determine the Point of Measurement must all be on the front of the ODR Source.
Those familiar with the arts of Image Metrology are also acquainted the Cosine Ambiguity. The Cosine Ambiguity is illustrated with the aid of FIGS. 3-8. FIG. 3 shows a possible pattern of Landmarks on an ODR Source. The ODR Source comprises a Transparent Substrate (120), Central Landmark (221), and another Landmark (222). A camera (140) acquires an image which is then analyzed. Possible orientations of target corresponding to φ=−30 degrees, φ=0 degrees and φ=+30 degrees are seen in FIG. 4 at 131, 132 and 133, respectively. If the Central Landmark (221) and another Landmark (222a) are all on the Front Face (121) of the Transparent Substrate (120) as shown in FIG. 5, then the rotation produces foreshortening along the axis of rotation (150) as shown in FIG. 6. However, the constellation of Landmarks has essentially the same appearance whether the angle is positive or negative, as seen in FIG. 6 at 141a and 143a, with 142 showing an angle of 0 degrees.
Mathematically, the essentially identical constellation of Landmarks is reflected in the fact that the arc-cosine function has two possible solutions. Consider, for example if it is determined by analysis of the locations of Landmarks in an image that the tilt angle φ of an ODR Source corresponds to cos(φ)=0.8660. We then find two possible solutions for angle φ, because both cos (−30°)=0.8660 and cos (30°)=0.8660. Said another way, the solution of the arc-cosine function is ambiguous.
In the field of Image Metrology, this ambiguity is referred to as the Cosine Ambiguity, and the two possible solutions are referred to as the two Branches of the Cosine Ambiguity, and Resolving the Cosine Ambiguity refers to determining the correct branch of the solution, which is to say the correct sign of the angles of the orientation measurement. The prior art ODR Sources offer no convenient means to Resolve the Cosine Ambiguity. Methods to Resolve the Cosine Ambiguity are known to the field of Image Metrology, but require that a feature, such as a ball on a stem, be added to the ODR Source. A ball on a stem is exposed to being knocked off, and greatly limits the utility of ODR-based orientation measurement in fields such as industrial automation or sports medicine.